The two values when the provided quadratic equation is solved for the x are -4.41 and -1.59 to the nearest hundredth.
<h3>What is a quadratic equation?</h3>
A quadratic equation is the equation in which the unknown variable is one and the highest power of the unknown variable is two.
The standard form of the quadratic equation is,
![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
Here, (<em>a,b,c</em>) are the real numbers and <em>x </em>is the variable.
To find the value of x, the following formula is used,
![x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
The given equation is,
![2(x+ 3)^2 - 4 = 0](https://tex.z-dn.net/?f=2%28x%2B%203%29%5E2%20-%204%20%3D%200)
To solve this equation, we need to apply some mathematical operations over it. Let's start with opening the brackets.
![2(x+ 3)^2 - 4 = 0\\2(x^2+6x+9)-4=0\\2x^2+12x+14-4\\2x^2+12x+12=0\\x^2+6x+7=0](https://tex.z-dn.net/?f=2%28x%2B%203%29%5E2%20-%204%20%3D%200%5C%5C2%28x%5E2%2B6x%2B9%29-4%3D0%5C%5C2x%5E2%2B12x%2B14-4%5C%5C2x%5E2%2B12x%2B12%3D0%5C%5Cx%5E2%2B6x%2B7%3D0)
On comparing with standard equation we get,
![a=1, b=6, c=7](https://tex.z-dn.net/?f=a%3D1%2C%20b%3D6%2C%20c%3D7)
Put this values in the above formula,
![x=\dfrac{-(6)\pm\sqrt{(6)^2-4(1)(7)}}{2(1)}\\x=\dfrac{-(6)\pm\sqrt{(6)^2-4(1)(7)}}{2(1)}\\x=-4.41,-1.59](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-%286%29%5Cpm%5Csqrt%7B%286%29%5E2-4%281%29%287%29%7D%7D%7B2%281%29%7D%5C%5Cx%3D%5Cdfrac%7B-%286%29%5Cpm%5Csqrt%7B%286%29%5E2-4%281%29%287%29%7D%7D%7B2%281%29%7D%5C%5Cx%3D-4.41%2C-1.59)
Hence, the two values when the provided quadratic equation is solved for the x are -4.41 and -1.59 to the nearest hundredth.
Learn more about the quadratic equation here;
brainly.com/question/1214333